Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×D251 | C2 | semidirect |
| 2. C2×#22548744 | C2 | semidirect |
| 4. #30631845 | C2 | semidirect |
| 5. #30631844 | C2 | semidirect |
| 6. #30631843 | C2 | semidirect |
| 7. #30631825 | C2 | semidirect |
| 8. #30631824 | C2 | semidirect |
| 9. #30631694 | C2 | semidirect |
| 10. #30631649 | C2 | semidirect |
| 11. #448×C251 | C2 | semidirect |
| 23. C2×Dic1004 | C22 | semidirect |
| 24. C2×#16860800 | C22 | semidirect |
| 25. C2×#16860798 | C22 | semidirect |
| 35. #22548640 | C22 | semidirect |
| 36. #22548639 | C22 | semidirect |
| 37. #22548638 | C22 | semidirect |
| 41. C2×SD16×C251 | C22 | semidirect |
| 43. #103×C251 | C22 | semidirect |
| 59. Q8×D251 | D4 | semidirect |
| 144. C22×C251 | #137 | semidirect |
| 152. C2×D251 | #137 | semidirect |
| 169. C251 | #3004 | semidirect |
| 179. #448 | D251 | semidirect |
| 197. C2×SD16 | C2×D251 | semidirect |
| 211. #103 | C2×D251 | semidirect |
| 321. C22 | #22548744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D251 | 2 |
| C2×#22548744 | 2 |
| #30632197 | 2 |
| #30631845 | 2 |
| #30631844 | 2 |
| #30631843 | 2 |
| #30631825 | 2 |
| #30631824 | 2 |
| #30631694 | 2 |
| #30631649 | 2 |
| #448×C251 | 2 |
| #3004 | 251 |